[ 66b ] 



LVIII. Some Problems relating to Rotating Fluid in the 

 Atmosphere. By George Green, D.Sc, Lecturer in 

 Natural Philosophy in the University of Glasgow* . 



ACCORDING to the modern view regarding the con- 

 stitution of cyclones and anticyclones the characteristic 

 movements of the air are in planes parallel to the earth's 

 surface. Upward currents may occur in certain parts of the 

 system, but they do not form the essential feature of the 

 motion. This view may, or may not, prove to be correct. 

 It is therefore a problem of some interest to determine under 

 what conditions horizontal motions of the type generally 

 associated with the normal cyclone and anticyclone are 

 possible in the atmosphere. Certain aspects of the problem 

 of the travelling cyclone have already been dealt with by 

 Dr. Jeffreys f, and by the late Lord Kayleigh J, and by 

 Sir Napier Shaw §. 



The present paper deals with the same problem in a 

 different way. Its purpose is to show that certain motions 

 of the type generally associated with the normal cyclone 

 are consistent with the hydrodynamieal equations of motion 

 and with the condition of continuity of the fluid, and 

 are therefore possible motions of the atmosphere. The 

 difficulty pointed out by the late Lord Rayleigh regarding 

 the boundary within which motion takes place, is not touched 

 upon in this paper. 



Let us assume that the air near any point at the earth's 

 surface is in uniform rotation relative to the earth about a 

 vertical axis OZ, drawn through upwards. This point 

 may be at rest or in motion relative to the earth while the 

 fluid layer in contact with the earth rotates uniformly 

 about as a centre of rotation. We can now refer the 

 motion of each particle of fluid to three rectangular axes 

 defined below drawn through the centre of the earth 0'. 



O'X is drawn parallel to a horizontal line drawn due 



East from point 0. 

 O'Y is drawn parallel to a horizontal line drawn due 



North from point 0. 

 O'Z is drawn parallel to a vertical line drawn through 



point 0. 



* Communicated by the Author. 



t Phil. Ma«-. January 1919, p. 1. 



\ Phil. Mag. September 1919, p. 420. 



§ Geophysical Memoirs of the Meteorological Office. 



